Proceedings of 37th Conference on Foundations of Computer Science (1996)
Oct. 14, 1996 to Oct. 16, 1996
F. Meyer auf der Heide , Dept. of Math. & Comput. Sci., Paderborn Univ., Germany
C. Scheideler , Dept. of Math. & Comput. Sci., Paderborn Univ., Germany
In this paper we present a deterministic protocol for routing arbitrary permutations in arbitrary networks. The protocol is analyzed in terms of the size of the network and the routing number of the network. Given a network H of size n, the routing number of H is defined as the maximum over all permutations /spl pi/ on [n] of the minimal number of steps to route /spl pi/ offline in H. We can show that for any network H of size n with routing number R our protocol needs O(log/sub R/ n/spl middot/R) time to route any permutation in H using only constant size edge buffers. This significantly improves all previously known results on deterministic routing. In particular our result yields optimal deterministic routing protocols for arbitrary networks with diameter /spl Omega/(n/sup /spl epsiv//) or bisection width O(n/sup 1-/spl epsiv//), /spl epsiv/>0 constant. Furthermore we can extend our result to deterministic compact routing. This yields, e.g., a deterministic routing protocol with runtime O((log n)/(log log n) R) for arbitrary bounded degree networks if only O(log n) bits are available at each node for storing routing information. Our proofs use a new protocol for routing arbitrary r/spl middot/s-relations in r-replicated s-ary Multibutterflies in optimal time O(log, n).
multiprocessor interconnection networks; deterministic routing; bounded buffers; online protocols; deterministic protocol; arbitrary permutations; arbitrary networks; r-replicated s-ary Multibutterflies
C. Scheideler and F. Meyer auf der Heide, "Deterministic routing with bounded buffers: turning offline into online protocols," Proceedings of 37th Conference on Foundations of Computer Science(FOCS), Burlington, VT, 1996, pp. 370.